Boundary-value problems for x-analytical functions with weighted boundary conditions

We consider boundary-value problems for x-analytical functions of a complex variable z = x + iy in a number of domains. Limit values with the weight (ln x)^–1 are given for the real part of the x-analytical function on the sections of the boundary that follow the imaginary axis, and simple limits are given for the real part of the x-analytical functions on the part of the boundary outside the imaginary axis. The apparatus of integral representations of x-analytical functions is applied to obtain a solution of the problem in quadratures.Kiev University. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 74, pp. 3–11, 1992;